In this thesis, we discuss the possibilities for suppression of decoherence, the loss of purity in an open quantum
system, and the related process of dephasing. In the first chapter, we review the literature on the subject
of open system dynamics, decoherence and methods of decoherence suppression. In the second chapter, we
focus on the specific case of a rotationally hot diatomic molecule as an example of an open quantum system,
where molecular vibrational wavepackets are subject to dephasing due to rovibrational coupling. We report
analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment
of the initial wavepacket phases. It appears that over long timescales, phase-only control is not possible,
but for earlier timescales the possibility of phase-only control of dephasing remains. In addition, we point
out that the time-dependence of the dephasing process depends significantly upon the degeneracy of the
rotational environment states. In the final chapter, we discuss the same system, but apply a qualitatively
different method of dephasing suppression based on the nonlinear resonance effect in a driving field. We
extend previous work on the topic (Shapiro et al. [1]) by considering the effect of using a train of laser pulses
as the driving field, in place of a two-colour continuous-wave laser field. We demonstrate that the pulse train
method can be more effective at suppressing dephasing than the two-colour CW case.